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| HAL: hal-00282893, version 1 |
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| Differential Integral Equations 22, 3-4 (2009) 303-320 |
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| Local well-posedness of nonlocal Burgers equations |
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Sylvie Benzoni-Gavage 1 |
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| (2009) |
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| This paper is concerned with nonlocal generalizations of the inviscid Burgers equation arising as amplitude equations for weakly nonlinear surface waves. Under homogeneity and stability assumptions on the involved kernel it is shown that the Cauchy problem is locally well-posed in $H^2(\R)$, and a blow-up criterion is derived. The proof is based on a priori estimates without loss of derivatives, and on a regularization of both the equation and the initial data. |
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| 1: | Institut Camille Jordan (ICJ) |
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CNRS : UMR5208 – Université Claude Bernard - Lyon I – Ecole Centrale de Lyon – Institut National des Sciences Appliquées de Lyon |
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| Subject | : | Mathematics/Analysis of PDEs |
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| Nonlinear surface wave – amplitude equation – smooth solutions – blow-up criterion. |
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| Attached file list to this document: | |||||
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| hal-00282893, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00282893 | |
| oai:hal.archives-ouvertes.fr:hal-00282893 | |
| From: Sylvie Benzoni-Gavage | |
| Submitted on: Wednesday, 28 May 2008 16:53:25 | |
| Updated on: Monday, 11 July 2011 10:39:30 | |
